.The high magnetic permeability of the individual filings causes their magnetic fields to concentrate at their ends.^The magnetic relative permeability (mu) for Iron at extremely high temperatures and pressures is not accurately known, but it seems to rise with temperature and seems certain to be at least 10,000.

.The mutual attraction of opposite poles then results in the formation of elongated clusters of filings along the field lines.^(In this way, they resemble the field lines of an iron bar magnet, which arch from the north to the south poles.

However, these lines do not precisely represent the field lines of the magnet, as the presence of the iron filings somewhat alters its magnetic field.

.Magnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges.^This electric field is not created by charges .

.For the physics of magnetic materials, see magnetism and magnet, more specifically ferromagnetism, paramagnetism, and diamagnetism.^FIELD OF THE INVENTION [0001] The present invention relates to a magnetic field control method and a magnetic field generator, and more specifically, to a magnetic field control method and a magnetic field generator in which an orientation of a magnetic field at a target position is changed to an arbitrary direction.

^Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

^The magnetic field generator according to claim 3 or 4, wherein at least one of the magnetic field generating units is constituted by a plurality of permanent magnets and a holding member holding the permanent magnets.

.A changing magnetic field generates an electric field and a changing electric field results in a magnetic field.^The relationship between the change in the magnetic field, and the electric field it produces.

.In view of special relativity, the electric and magnetic fields are two interrelated aspects of a single object, called the electromagnetic field.^Melatonin aspects of exposure to low frequency electric and magnetic fields.

.A pure electric field in one reference frame is observed as a combination of both an electric field and a magnetic field in a moving reference frame.^Where is the moving charge responsible for this magnetic field?

.In modern physics, the magnetic (and electric) fields are understood to be due to a photon field; in the language of the Standard Model the electromagnetic force is mediated by photons.^H-field alias magnetizing force .

.Most often this microscopic description is not needed because the simpler classical theory covered in this article is sufficient; the difference is negligible under most circumstances.^This article proposes a comprehensive theory that logically explains ALL the peculiar findings, as well as a mathematically and physically logical description of the source itself.

^Magnetic Grid Layer After extensive research into magnetic fields and the use of magnets in alternative health care, engineers designed a magnetic grid pattern with two distinct benefits: First, the field distribution is even, so that all parts of the body benefit equally.

[2] There are many alternative names for both, though. (See sidebar.) .To avoid confusion, this article uses B-field and H-field for these fields, and uses magnetic field where either or both fields apply.^B = 0 Maxwell's Equation for B You could argue that B indicates better the strength of a magnetic field than does the 'magnetic field strength' H! This is one reason why modern authors tend not to use these names and stick instead with 'B field' and 'H field'.

.The B-field can be defined in many equivalent ways based on the effects it has on its environment.^MR ( magnetoresistive ) A technology based on the effect where electrical resistance in a material changes when brought in contact with a magnetic field .

where × is the vector cross product. .The B-field is measured in teslas in SI units and in gauss in cgs units.^The unit of magnetic field, the tesla, is named after Serbian-American inventor Nikola Tesla.

A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View...13 January 2010 10:13 UTCwww.knowthelies.com [Source type: FILTERED WITH BAYES]

^For these reasons, let's look at an alternative method of defining the magnetic field which, although not as fundamental or mathematically simple, may be more appealing.

^The effect occurs only when the magnetic field is changing, and it appears to be proportional to the derivative ∂ B /∂ t , which is in one direction when the field is being established, and in the opposite direction when it collapses.

H is defined as a modification of B due to magnetic fields produced by material media, such that (in SI):

where .M is the magnetization of the material and μ0 is the permeability of free space (or magnetic constant).^H = B / μ 0 - M Sommerfeld Field Equation This formula applies generally, even if the materials within the field have non-uniform permeability or a permanent magnetic moment .

^The result is that when a magnetic field enters a high-permeability material, it tends to twist abruptly to one side, and the pattern of the field tends to be channeled through the material like water through a funnel.

.In materials for which M is proportional to B the relationship between B and H can be cast into the simpler form: H = B/μ, where μ is a material dependent parameter called the permeability.^In fact, if you can treat the permeability as being linear, then the constants N , l e , μ and A e can be lumped together into one constant for the winding which is called (surprise!

.For many materials, though, there is no simple relationship between B and M.^Though studies are being done to see if there is a link between it and tumors of the brain and central nervous system, there is no definitive link between the two, the institute says on its Web site.

.For example, ferromagnetic materials and superconductors have a magnetization that is a multiple-valued function of B due to hysteresis.^Since the hysteresis curve is nonlinear, and is not a function (it has more than one value of M for a particular value of B ), a ferromagnetic material does not have a single, well-defined value of the permeability μ; a value like 4,000 for transformer iron represents some kind of a rough average.

.They are made of ferromagnetic materials such as iron and nickel that have been magnetized.^Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.

^I suggested that if such motions were fast enough, they could cause magnetic polarity reversals.

The Earths Magnetic Field is Still Losing Energy13 January 2010 10:13 UTCwww.creationresearch.org [Source type: Academic]

^Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

.The strength of a magnet is represented by its magnetic moment, m; for simple magnets, m points in the direction of a line drawn from the south to the north pole of the magnet.^That is, it is not a simple field with just a north and south pole, like a bar magnet.

Force on a magnet due to a non-uniform B

.Like magnetic poles brought near each other repel while opposite poles attract.^Worse yet, the various movements of the location of the two Magnetic Poles often seem to have no relationship with each other.

.This is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) to regions of higher magnetic field.^However, Barnes also argues strenuously against the standard theory of dynamo action generating the Earth's magnetic field.

.For example, opposite poles attract because each magnet is pulled into the larger magnetic field near the pole of the other; the force is attractive because for each magnet m is in the same direction as the magnetic field B of the other.^Infer the direction of the magnetic field.

.Reversing the direction of m reverses the resultant force.^Make a sketch showing the direction of motion and the direction of the field, and show that the resulting force is in the right direction to produce circular motion.

.Magnets with m opposite to B are pushed into regions of lower magnetic field, provided that the magnet, and therefore, m does not flip due to magnetic torque.^The torque on a current loop in a magnetic field.

^Having two poles, one north and one south, it has the same shape as the field from a tiny but powerful bar magnet right at the center of the sphere.

The Earths Magnetic Field is Still Losing Energy13 January 2010 10:13 UTCwww.creationresearch.org [Source type: Academic]

.The ability of a nonuniform magnetic field to sort differently oriented dipoles is the basis of the Stern–Gerlach experiment, which established the quantum mechanical nature of the magnetic dipoles associated with atoms and electrons.^But the nature of the field is evident in all magnetic fields.

Mathematically, the force on a magnet having a magnetic moment m is:[8]

where the .gradient∇ is the change of the quantity m · B per unit distance and the direction is that of maximum increase of m · B.^As the gradiometer rod was turned away from the direction of maximum frequency (maximum gradient), i.e., rotated to the left, right, upward or downward, the frequency decreased considerably.

.(The dot productm · B = mBcos(θ), where m and B represent the magnitude of the m and B vectors and θ is the angle between them.^The energy density of a light wave is related to the magnitudes of the fields in a specific way --- it depends on the squares of their magnitudes, E 2 and B 2 , which are the same as the dot products E ⋅ E and B ⋅ B .

) .This equation is strictly only valid for magnets of zero size, but it can often be used as an approximation for not too large magnets.^An infinite magnetic circulation Γ B can only be produced by an infinite magnetic field, so without the ∂Φ E /∂ t term, Maxwell's equations predict nonsense: the edge of the surface would experience an infinite magnetic field at one instant, and zero magnetic field at all other times.

.The magnetic force on larger magnets is determined by dividing them into smaller regions having their own m then summing up the forces on each of these regions.^Plugging all these values into the equation gives a result of a Magnetic Flux of around 4 * 10 25 Maxwells.

.The force between two magnets is quite complicated and depends on the orientation of both magnets and the distance of the magnets relative to each other.^Find the induced magnetic field at a point between the plates, at a distance R from the axis.

.The force is particularly sensitive to rotations of the magnets due to magnetic torque.^One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

.In many cases, the force and the torque on a magnet can be modeled quite well by assuming a 'magnetic charge' at the poles of each magnet and using a magnetic equivalent to Coulomb's law.^These lodestones have been charged by the Earth, and thus are harmoniously in tune with the human bodies' frequencies as well, they have for thousands of years been successfully used in the healing arts.

^The fact that this theory suggests that the Earth's Magnetic Field measured at the surface (or in space) is a result of the vector sum of two much stronger but generally opposing source fields, enables straightforward explanation of many of the peculiar characteristics measured in the Earth's Magnetic Field.

.An external H-field exerts a force in the direction of H on a north pole and opposite to H on a south pole.^Today, the magnetic field focuses space radiation towards the far north and south where few people live.

^By symmetry, the field in this plane cannot have any component in the radial direction (inward toward the dipole, or outward away from it); it is perpendicular to the plane, and in the opposite direction compared to the dipole vector.

^If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

.Unfortunately, the idea of "poles" does not accurately reflect what happens inside a magnet (see ferromagnetism).^The present premise does NOT require this, and includes a mechanism for explaining the separation of the Geographic and Magnetic Poles.

.For instance, a small magnet placed inside of a larger magnet feels a force in the opposite direction.^Humans have an innate ability to sense the direction of magnetic north, and this ability can be blocked by placing a bar magnet against a person's forehead for only fifteen minutes!

^Likewise, as shown in figure f , if we could find the magnetic field of a square dipole, then we could find the field of any planar loop of current by adding the contributions to the field from all the squares.

.This phenomenon explains why the magnetic needle of a compass points toward the Earth's north pole.^However, a compass needle doesn't point at true north, at the real geographical North Pole, instead it points at magnetic north.

.Magnetic torque is used to drive simple electric motors.^An electric motorized clock, plugged into a wall socket, produces an amazingly high magnetic field because of the small electric motor that runs it.

.In one simple motor design, a magnet is fixed to a freely rotating shaft (forming a rotor) and subjected to a magnetic field from an array of electromagnets—called the stator.^A magnetic field in the form of a sine wave.

.By continuously switching the electrical current through each of the electromagnets, thereby flipping the polarity of their magnetic fields, the stator keeps like poles next to the rotor; The resultant magnetic torque is transferred to the shaft.^In particular, the fact that electric currents create magnetic fields.

.The inverse process, changing mechanical motion to electrical energy, is accomplished by the inverse of the above mechanism in the electric generator.^These processes use artificial electrical energy, which has within its structure a frequency composition different to that of nature.

^MARIO ACUNA: So here is my spring, here's my magnet, and if I pass an electrical current through my spring and measure the disturbance of my magnet, which is inside, then I can transmit back to Earth the information about the strength and the direction of the field we are trying to measure.

.Then mark each location with an arrow (called a vector) pointing in the direction of the local magnetic field with a length proportional to the strength of the magnetic field.^Infer the direction of the magnetic field.

As seen here, the magnetic field points towards a magnet's south pole and away from its north pole.

.Various physical phenomena have the effect of displaying magnetic field lines.^MR ( magnetoresistive ) A technology based on the effect where electrical resistance in a material changes when brought in contact with a magnetic field .

.For example, iron filings placed in a magnetic field line up in such a way as to visually show the orientation of the magnetic field (see figure to left).^Figure 1a shows the magnetic lines of force outside a magnetized sphere.

The Earths Magnetic Field is Still Losing Energy13 January 2010 10:13 UTCwww.creationresearch.org [Source type: Academic]

.Magnetic fields lines are also visually displayed in polar auroras, in which plasma particle dipole interactions create visible streaks of light that line up with the local direction of Earth's magnetic field.^The earth's magnetic field impacts climate .

A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View...13 January 2010 10:13 UTCwww.knowthelies.com [Source type: FILTERED WITH BAYES]

^If the sample is initially unmagnetized, 1, and a field H is externally applied, the magnetization increases, 2, but eventually becomes saturated, 3, so that higher fields do not result in any further magnetization, 4.

.Field lines are also a good qualitative tool for visualizing magnetic forces.^Figure 1a shows the magnetic lines of force outside a magnetized sphere.

The Earths Magnetic Field is Still Losing Energy13 January 2010 10:13 UTCwww.creationresearch.org [Source type: Academic]

^For a purely dipolar field, the equation r = R sin 2 q relates the radius r and colatitude q of each point on a given line of force, R being the value of r where the line of force intersects the equatorial plane.

The Earths Magnetic Field is Still Losing Energy13 January 2010 10:13 UTCwww.creationresearch.org [Source type: Academic]

^It is that a magnetic field is a primary force in the same way as gravity is seen as a primry force.

.In ferromagnetic substances like iron and in plasmas, magnetic forces can be understood by imagining that the field lines exert a tension, (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines.^Treatment with the iron chelator deferiprone also blocked the effects of magnetic fields on brain cell DNA, suggesting the involvement of iron.

.'Unlike' poles of magnets attract because they are linked by many field lines; 'like' poles repel because their field lines do not meet, but run parallel, pushing on each other.^Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

^For reasons not fully understood, CMEs in even-numbered solar cycles (like 24) tend to hit Earth with a leading edge that is magnetized north.

A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View...13 January 2010 10:13 UTCwww.knowthelies.com [Source type: FILTERED WITH BAYES]

.The opposite occurs for a compass placed near a magnet's south pole.^When the Voyager II space probe flew past Uranus and Neptune, the apparent north and south magnetic poles were sizably offset from where the rotational pole was in earlier recordings.

A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View...13 January 2010 10:13 UTCwww.knowthelies.com [Source type: FILTERED WITH BAYES]

^That is, it is not a simple field with just a north and south pole, like a bar magnet.

.Not all magnetic fields are describable in terms of poles, though.^All matter on Earth assists in creating this field and so becomes charged with this magnetic resonance, displaying different results, dependant on the substance.

^They suggests that specific tones described as g-mode vibrations are picked up by the magnetic field at the Sun’s surface.

A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View...13 January 2010 10:13 UTCwww.knowthelies.com [Source type: FILTERED WITH BAYES]

.A straight current-carrying wire, for instance, produces a magnetic field that points neither towards nor away from the wire, but encircles it instead.^Scientists believe that just as the electric currents produce the magnetic field, so the magnetic field produces the electric currents.

B-field lines never end

.Field lines are a useful way to represent any vector field and often reveal sophisticated properties of fields quite simply.^The Russian National Academy of Sciences doesn't give us a time-line, but the change from what was known and accepted to the way it is now represents a 1000 percent increase.

A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View...13 January 2010 10:13 UTCwww.knowthelies.com [Source type: FILTERED WITH BAYES]

^A vector going into the page is represented using the tailfeathers of the arrow.

.One important property of the B-field is that it is a solenoidal vector field.^We could, for example, have two solenoidal coils, one in the outgoing line and one in the return line, interwound with one another with their windings oriented so that their differential-mode fields would cancel.

.In field line terms, this means that magnetic field lines neither start nor end: They always either form closed curves ("loops"), or extend to and from infinity.^The torque on a current loop in a magnetic field.

.Magnetic field exits a magnet near its north pole and enters near its south pole but inside the magnet B-field lines return from the south pole back to the north.^That is, it is not a simple field with just a north and south pole, like a bar magnet.

^In the language of space physics, a north-pointing solar magnetic field is called a "northern IMF" and it is synonymous with shields up.

A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View...13 January 2010 10:13 UTCwww.knowthelies.com [Source type: FILTERED WITH BAYES]

.For this reason, magnetic poles always come in N and S pairs.^(Recall that the radio beams in an ordinary pulsar come from a rotation-driven outflow of charged particles above the magnetic poles.

.Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits.^An electric current flowing in a wire or coil produces its own magnetic field.

.The SI unit for magnetic field is the tesla, which can be seen from the magnetic part of the Lorentz force law Fmag = (qv × B) to be equivalent to (newton × second)/(coulomb × metre).^GARY GLATZMAIER: Now this movie will show part of a simulation that spans a magnetic field reversal.

^If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

Magnetic monopole (hypothetical)

.A magnetic monopole is a hypothetical particle (or class of particles) that has, as its name suggests, only one magnetic pole (either a north pole or a south pole).^Today, the magnetic field focuses space radiation towards the far north and south where few people live.

^This buildup of charge would start to quench both currents due to electrical forces, but the current in the right side of the wire, which is driven by the weaker magnetic field, would be the first to stop.

.Modern interest in this concept stems from particle theories, notably Grand Unified Theories and superstring theories, that predict either the existence or the possibility of magnetic monopoles.^Both possibilities are probable, and in either event they would lose their structure as a string and collapse into a field of dissassociated particles, half of which would be manifest as truants.

^Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

^MARIO ACUNA: So here is my spring, here's my magnet, and if I pass an electrical current through my spring and measure the disturbance of my magnet, which is inside, then I can transmit back to Earth the information about the strength and the direction of the field we are trying to measure.

.Whether inside or out of a magnet, H-field lines start near the S pole and end near the N. The H-field, therefore, is analogous to the electric field E which starts as a positive charge and ends at a negative charge.^This electric field is not created by charges .

.It is tempting, therefore, to model magnets in terms of magnetic charges localized near the poles.^In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

[13].Moving point charges, such as electrons, produce complicated but well known magnetic fields that depend on the charge, velocity, and acceleration of the particles.^The electric field at point P is , and the magnetic field is .

.The direction of such a magnetic field can be determined by using the "right hand grip rule" (see figure at right).^In general, determine these plus and minus signs using the right-hand rule shown in the figure.

.The strength of the magnetic field decreases in inverse proportion to the square of the distance from the conductor (inverse-square law).^Its strength is proportional to the rate at which the field changes.

.Bending a wire into multiple closely-spaced loops to form a coil or "solenoid" enhances this effect.^Problem 33 dealt with the dependence of a transformer's gain on the number of loops of wire in the input solenoid.

.A finite length electromagnet produces essentially the same magnetic field as a uniform permanent magnet of the same shape and size, with its strength and polarity determined by the current flowing through the coil.^Scientists believe that just as the electric currents produce the magnetic field, so the magnetic field produces the electric currents.

The magnetic field generated by a steady[15]currentI (a constant flow of charges in which charge is neither accumulating nor depleting at any point) is described by the Biot–Savart law:

where the integral sums over the entire loop of a wire with .dℓ a particular infinitesimal piece of that loop, μ0 is the magnetic constant, r is the distance between the location of dℓ and the location at which the magnetic field is being calculated, and is a unit vector in the direction of r.^What is the difference between an electric field and a magnetic field?

A slightly more general[16][17] way of relating the current I to the B-field is through Ampère's law:

where the integral is over any arbitrary loop and Ienc is the current enclosed by that loop. .Ampère's law is always valid for steady currents and can be used to calculate the B-field for certain highly symmetric situations such as an infinite wire or an infinite solenoid.^But we can build just about any static current distribution we like using such a bundle of wires, so it follows that Ampère's law is valid for any static current distribution.

.In a modified form that accounts for time varying electric fields, Ampère's law is one of four Maxwell's equations that describe electricity and magnetism.^The Φ E equation is Gauss' law: charges make diverging electric fields.

Force due to a B-field on a moving charge

Force on a charged particle

Beam of electrons moving in a circle. Lighting is caused by excitation of atoms of gas in a bulb.

.A charged particle moving in a B-field experiences a sideways force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle.^When charged particles are moving, they make magnetic fields as well.

where .F is the force, q is the electric charge of the particle, v is the instantaneous velocity of the particle, and B is the magnetic field (in teslas).^This electric field is not created by charges .

^Suppose a charged particle is moving through a region of space in which there is an electric field perpendicular to its velocity vector, and also a magnetic field perpendicular to both the particle's velocity vector and the electric field.

.For that reason, charged particles move in a circle (or more generally, in a helix) around magnetic field lines; this is called cyclotron motion.^Where is the moving charge responsible for this magnetic field?

.Because the magnetic force is always perpendicular to the motion, the magnetic fields can do no work on an isolated charge.^Because the other studies reporting effects of magnetic fields on DNA were carried out under continuous exposure conditions, the results of Ivancsits et al.

.It can and does, however, change the particle's direction, even to the extent that a force applied in one direction can cause the particle to drift in a perpendicular direction.^The magnetic force is always perpendicular to the motion of the particle, so it can never do any work, and a charged particle moving through a magnetic field does not experience any change in its kinetic energy: its velocity vector can change its direction, but not its magnitude.

.It is often claimed that the magnetic force can do work to a non-elementary magnetic dipole, or to charged particles whose motion is constrained by other forces, but this is not the case[18] because the work in those cases is performed by the electric forces of the charges deflected by the magnetic field.^Note that the magnetic field never does work on a charged particle, because its force is perpendicular to the motion; the electric power is actually coming from the mechanical work that had to be done to spin the coil.

Force on current-carrying wire

.The force on a current carrying wire is similar to that of a moving charge as expected since a charge carrying wire is a collection of moving charges.^The moving charges in the wire attract the moving charges in the electron beam, causing the electrons to curve.

^This buildup of charge would start to quench both currents due to electrical forces, but the current in the right side of the wire, which is driven by the weaker magnetic field, would be the first to stop.

.The Lorentz force on a macroscopic current is often referred to as the Laplace force.^There is no induction going on in this frame of reference; the forces that cause the current are just the ordinary magnetic forces experienced by any charged particle moving through a magnetic field.

The right-hand rule: Pointing the thumb of the right hand in the direction of the conventional current or moving positive charge and the fingers in the direction of the B-field the force on the current points out of the palm.^Where is the moving charge responsible for this magnetic field?

See the figure on the right. .Using the right hand and pointing the thumb in the direction of the moving positive charge or positive current and the fingers in the direction of the magnetic field the resulting force on the charge points outwards from the palm.^The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

.If both the speed and the charge are reversed then the direction of the force remains the same.^If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

.For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left.^When charged particles are moving, they make magnetic fields as well.

.(Both of these cases produce the same current.^We can produce these currents by tiling the region between the circles with square current loops, whose currents all cancel each other except at the inner and outer edges.

) .On the other hand, a magnetic field combined with an electric field can distinguish between these, see Hall effect below.^The relationship between the change in the magnetic field, and the electric field it produces.

.A magnetic material placed inside a magnetic field, though, generates its own bound current which can be a challenge to calculate.^What is the magnetic field inside a long, straight wire in which the current density is j ?

.(This bound current is due to the sum of atomic sized current loops and the spin of the subatomic particles such as electrons that make up the material.^The field of a square-loop dipole is very complicated close up, but luckily for us, we only need to know the current at distances that are large compared to the size of the loop, because we're free to make the squares on our grid as small as we like.

Magnetization

.The magnetization field M represents how strongly a region of material is magnetized and is defined as the volume density of the net magnetic dipole moment in that region.^Example 1: The magnetic dipole moment of an atom .

.The unit of magnetization M in SI is ampere-turn per meter which is identical to that of the H-field since the unit of magnetic moment is ampere-turn m2.^The ambient magnetic field in our laboratory (i.e., when the power supply to the coils was turned off) was 0.14 T. .

.Magnetization can be thought of as the magnetic equivalent of the polarization densityP used for electrical charges.^In: 1997 Annual Review of Research on Biological Effects of Electric and Magnetic Fields from the Generation, Delivery, and Use of Electricity.

.In other words, M begins and ends at bound magnetic charges.^Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

.(Unlike B, magnetization must begin and end near the poles; there is no magnetization outside of the material.^Also, as there is no change to the weight of a magnet as a result of this movement of flux then one may conclude that the actual quantity of that flux may be constant.

.An equivalent, and more physically correct, way to represent magnetization is to add all of the currents of the dipole moments that produce the magnetization.^Example 1: The magnetic dipole moment of an atom .

See #Magnetic dipoles below and magnetic poles vs. atomic currents for more information. The resultant current is called bound current and is the source of the magnetic field due to the magnet. Mathematically, the curl of M equals the bound current.

^If the sample is initially unmagnetized, 1, and a field H is externally applied, the magnetization increases, 2, but eventually becomes saturated, 3, so that higher fields do not result in any further magnetization, 4.

.The term magnetism is used to describe how these materials respond on the microscopic level and is used to categorize the magnetic phase of a material.^Living organisms have the ability to somehow sense these minute daily cycles in the Earth's magnetic field and to use them to time their biological cycles.

.They also are highly magnetic and can be perfect diamagnets below a lower critical magnetic field.^Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

Superconductors often have a broad range of temperatures and magnetic fields (the so named mixed state) for which they exhibit a complex hysteretic dependence of M on B.

H-field and magnetic materials

In the case of paramagnetism, and diamagnetism the magnetization M is often proportional to the applied magnetic field such that:

where .μ is a material dependent parameter called the permeability (see constitutive equations).^We need to organize our knowledge about the properties that materials can possess, and see whether this knowledge allows us to calculate anything useful with Maxwell's equations.

.In some cases the permeability may be a second rank tensor so that H may not point in the same direction as B.^Consider the configuration where the small one is inside the big one with their currents circulating in the same direction, and a second configuration in which the currents circulate in opposite directions.

These relations between B and H are examples of constitutive equations. .However, superconductors and ferromagnets have a more complex B to H relation, see hysteresis.^However, having said that there is the chance that, at it's worst - it might entertain a purist to see the bazaar machinations of thought applied by an outsider to the complexity of the forces.

.The advantage of the H-field is that its bound sources are treated so differently that they can often be isolated from the free sources.^Magnetic field significantly different from sham at p < 0.01 in vehicle-treated animals.

where the equation has been rearranged so that its parallel to the displacement field is more obvious. .Noting that −∇ · μ0M = ρb the bound magnetic charge density from the definition of M above and that ∇ · B = 0 represents the absence of free magnetic charges this definition of H requires that μ0∇ · H = ρtot.^In other words, the total charge, q , appearing in Maxwell's equartions is actualy q = q free - q bound , where q free is the charge that moves freely through wires, and can be detected in an ammeter, while q bound is the charge bound onto the individual molecules, which can't.

.In other words, as described above, the definition of H requires that its field lines begin at positive magnetic charge (near south pole) and end at a negative magnetic charge (north pole).^Where is the moving charge responsible for this magnetic field?

Energy stored in magnetic fields

.In asking how much energy is needed to create a specific magnetic field using a particular current it is important to distinguish between free and bound currents.^What is the difference between an electric field and a magnetic field?

.The bound currents create a magnetic field that the free current has to work against without doing any of the work.^The current in the first wire creates a magnetic field that acts on the current in the second wire.

.Nonlinear materials cannot use the above equation but must return to the first equation which is always valid.^We need to organize our knowledge about the properties that materials can possess, and see whether this knowledge allows us to calculate anything useful with Maxwell's equations.

.In particular, the energy density stored in the fields of hysteretic materials such as ferromagnets and superconductors depends on how the magnetic field was created.^Do we have infinite energy in the resulting magnetic field?

where .J is the current density, and partial derivatives indicate spatial location is fixed when the time derivative is taken.^If the particle is pointlike, then it takes zero time to pass any particular location, and the current is then infinite at that point in space.

The last term is Maxwell's correction. .This equation is valid even when magnetic materials are involved, but in practice it is often easier to use an alternate equation.^An easy way to approach this is to use the fact that vB has the same units as E , which can be seen by comparing the equations for magnetic and electric forces used above.

^Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

^The relationship Γ E ∝ -∂ B /∂ t tells us that a changing magnetic field creates an electric field in the surrounding region of space, but the phrase “surrounding region of space” is vague, and needs to be made mathematical.

.The inverse process also occurs: a changing magnetic field, such as a magnet moving through a stationary coil, generates an electric field (and therefore tends to drive a current in the coil).^The electric field of a sheet of charge, and the magnetic field of a sheet of current.

.(These two effects bootstrap together to form electromagnetic waves, such as light.^X-ray photons traveling through such strong fields readily split into two, or merge together; and many other novel physical effects come into play.

where . is the electromotive force (or EMF, the voltage generated around a closed loop) and Φm is the magnetic flux—the product of the area times the magnetic field normal to that area.^The torque on a current loop in a magnetic field.

.(This definition of magnetic flux is why engineers often refer to B as "magnetic flux density".) This law includes both flux changes because of the magnetic field generated by a time varying E-field (transformer EMF) and flux changes because of movement through a magnetic field (motional EMF).^Both of these fields change over time, however.

A form of Faraday's law of induction that does not include motional EMF is the Maxwell–Faraday equation:

one of Maxwell's equations. .This equation is valid even in the presence of magnetic material.^Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

Maxwell's equations

.Like all vector fields the B-field has two important mathematical properties that relates it to its sources.^We find ourselves in a region where the field is very much as it was before, except that all the field vectors have had one unit worth of added to them.

.Maxwell's Equations together with the Lorentz force law form a complete description of classical electrodynamics including both electricity and magnetism.^A complete statement of Maxwell's equations in the presence of electric and magnetic materials is as follows: .

^This buildup of charge would start to quench both currents due to electrical forces, but the current in the right side of the wire, which is driven by the weaker magnetic field, would be the first to stop.

.The first property is the divergence of a vector field A, ∇ · A which represents how A 'flows' outward from a given point.^By symmetry, the field in this plane cannot have any component in the radial direction (inward toward the dipole, or outward away from it); it is perpendicular to the plane, and in the opposite direction compared to the dipole vector.

.As discussed above a B-field line never starts nor ends at a point but instead forms a complete loop.^Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

.The electric field on the other hand begins and ends at electrical charges so that its divergence is non-zero and proportional to the charge density (See Gauss's law).^The Φ E equation is Gauss' law: charges make diverging electric fields.

Diagram showing how the magnetic field is a pseudovector: A loop of wire (black), carrying a current, creates a magnetic field (blue).^Any wire that carries an AC electrical current produces magnetic fields.

.When the wire is reflected in a mirror (dotted line), the magnetic field it generates is not reflected in the mirror: Instead, it is reflected and reversed.^Non-localized fields due to household wiring are usually highest in the room next to where the power line connects or where there is a circuit breaker panel.

where .J = complete microscopic current density and ρ is the charge density.^Let's model the current in wire 2 by pretending that there is a line charge inside it, possessing density per unit length λ 2 and moving at velocity v 2 .

.Because of the right-hand rule, if a current-carrying loop were viewed in a mirror, the resulting B vector would be both mirror imaged and flipped in orientation, whereas an ordinary vector (e.g., velocity) would be mirror-imaged only.^This agrees with the right-hand rule.

.As discussed above, materials respond to an applied electric E field and an applied magnetic B field by producing their own internal 'bound' charge and current distributions that contribute to E and B but are difficult to calculate.^Shielding magnetic fields is more difficult than shielding electric fields.

.They also need to be supplemented by the relationship between B and H as well as that between E and D.^(To do this problem, you need to know the relativistic relationship between the energy and momentum of a beam of light.

.On the other hand, for simple relationships between these quantities this form of Maxwell's equations can circumvent the need to calculate the bound charges and currents.^At all other times (when charges are stable), no current flows.

Electric and magnetic fields: different aspects of the same phenomenon

.According to special relativity, the partition of the electromagnetic force into separate electric and magnetic components is not fundamental, but varies with the observational frame of reference; an electric force perceived by one observer is perceived by another (in a different frame of reference) as a mixture of electric and magnetic forces.^In her frame of reference, it's the bar magnet that is moving.

.More specifically, special relativity combines the electric and magnetic fields into a rank-2 tensor, called the electromagnetic tensor.^Shielding magnetic fields is more difficult than shielding electric fields.

Changing reference frames mixes these components. .This is analogous to the way that special relativity mixes space and time into spacetime, and mass, momentum and energy into four-momentum.^In this way, the energy of a magnetic twist outside a magnetar is gradually dissipated into X-rays.

Magnetic vector potential

.In advanced topics such as quantum mechanics and relativity it is often easier to work with a potential formulation of electrodynamics rather than in terms of the electric and magnetic fields.^Shielding magnetic fields is more difficult than shielding electric fields.

.The vector potential A may be interpreted as a generalized potential momentum per unit charge[26] just as φ is interpreted as a generalized potential energy per unit charge.^Let ±λ be the charge per unit length of each line charge without relativistic contraction, i.e., in the frame moving with that line charge.

.Maxwell's equations when expressed in terms of the potentials can be cast into a form that agrees with special relativity with little effort.^Now this is very subtle, because Maxwell's equations treat these charges on an equal basis, but in terms of practical measurements, they are completely different.

^Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

[27].In relativity A together with φ forms the four-potential analogous to the four-momentum which combines the momentum and energy of a particle.^If there wasn't this kind of consistency between the momentum and the energy, then we could violate conservation of momentum by combining light beams or splitting them up.

.Using the four potential instead of the electromagnetic tensor has the advantage of being much simpler; further it can be easily modified to work with quantum mechanics.^Also, the use of a power-conditioning outlet strip (specifying reduced electromagnetic interference) is recommended to avoid radio waves being picked up from the power line by the computer.

Quantum electrodynamics

.In modern physics, the electromagnetic field is understood to be not a classicalfield, but rather a quantum field; it is represented not as a vector of three numbers at each point, but as a vector of three quantum operators at each point.^Many fascinating physical effects occur in magnetic fields with strength exceeding the "quantum electrodynamic field strength" of B Q = 4.4 X 10 13 Gauss.

.These theories explain that the electromagnetic field is derived from the photon field; indeed, all electromagnetic interactions are mediated by this field.^The significant increase in these systems and their interactions with other energy fields in our homes, cars and work places will in fact be significantly increasing health risks.

.QED describes the electromagnetic interaction between charged particles (and their antiparticles) as due to the exchange of virtual photons.^Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

Predictions of QED agree with experiments to an extremely high degree of accuracy: currently about 10−12 (and limited by experimental errors); for details see precision tests of QED. .This makes QED one of the most accurate physical theories constructed thus far.^That wouldn't make sense, because there is no physical reason why one part of the wire would behave differently than any other.

All equations in this article are in the classical approximation, which is less accurate than the quantum description as mentioned above. However, under most everyday circumstances, the difference between the two theories is negligible.

Measuring the B-field

.Devices used to measure the local magnetic field are called magnetometers.^The magnetite crystals "tell" the pigeon's brain the exact direction of the Earth's magnetic field, and the pigeon uses this information to navigate with its amazing precision.

.The smallest magnetic field measured[29] is on the order of attoteslas (10−18 tesla); the largest magnetic field produced in a laboratory is 2,800 T (VNIIEF in Sarov, Russia, 1998)[30] The magnetic field of some astronomical objects such as magnetars are much higher; magnetars range from 0.1 to 100 GT (108 to 1011 T).^The spatial variation of the magnetic field is on the order of (10 9 T/10 4 m)=10 5 T/m.

History

One of the first drawings of a magnetic field, by René Descartes, 1644. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, "threaded parts", through threaded pores in magnets.

.Perhaps the earliest description of a magnetic field was performed by the French scholar Petrus Peregrinus and published in his Epistola Petri Peregrini de Maricourt ad Sygerum de Foucaucourt Militem de Magnete and is dated 1269 A.D. Petrus Peregrinus mapped out the magnetic field on the surface of a spherical magnet.^The arrows map the magnetic field B .

.Noting that the resulting field lines crossed at two points he named those points 'poles' in analogy to Earth's poles.^Momentum, however, is a vector, and there is only one physically meaningful way of multiplying two vectors to get a vector result, which is the cross product (see page 854).

^The core will reach saturation more quickly when the coil's field is in the same direction as the Earth's, but will not saturate as early in the next half-cycle, when the two fields are in opposite directions.

.Almost three centuries later, near the end of the sixteenth century, William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth itself was a magnet.^Simultaneously, the magnetic field rearranges itself to a state of lower energy.

William Gilbert's great work De Magnete was published in 1600 A.D. and helped to establish the study of magnetism as a science.

.The modern understanding that the B-field is the more fundamental field with the H-field being an auxiliary field was not easy to arrive at.^But with the advantage of modern hindsight, we can understand in fundamental terms the facts that Faraday had to take simply as mysterious experimental observations.

.Indeed, largely because of mathematical similarities to the electric field, the H-field was developed first and was thought at first to be the more fundamental of the two.^Observers in the two frames agree on how much force there is, so in the loop's frame, we have an electric field .

^The core will reach saturation more quickly when the coil's field is in the same direction as the Earth's, but will not saturate as early in the next half-cycle, when the two fields are in opposite directions.

.The modern distinction between the B- and H- fields was not needed until Siméon-Denis Poisson (1781–1840) developed one of the first mathematical theories of magnetism.^What is the difference between an electric field and a magnetic field?

.Poisson's model, developed in 1824, assumed that magnetism was due to magnetic charges.^A charged particle of mass m and charge q moves in a circle due to a uniform magnetic field of magnitude B , which points perpendicular to the plane of the circle.

^One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

.In modern notation, Poisson's model is exactly analogous to electrostatics with the H-field replacing the electric fieldE-field and the B-field replacing the auxiliary D-field.^This is the same as the field of a magnetic dipole in its midplane, except that the electric coupling constant k replaces the magnetic version k / c 2 , and the electric dipole moment D is substituted for the magnetic dipole moment m .

^Since some of the fields referred to in Maxwell's equations are the electric and magnetic fields E and B , while others are the auxiliary fields D and H , some of the constraints deal with E and B , others with D and H .

Poisson's model was, unfortunately, incorrect. .Magnetism is not due to magnetic charges.^A charged particle of mass m and charge q moves in a circle due to a uniform magnetic field of magnitude B , which points perpendicular to the plane of the circle.

^One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

The model, however, was remarkably successful for being fundamentally wrong. .It predicts the correct relationship between the H-field and the B-field, even though it wrongly places H as the fundamental field with B as the auxiliary field.^As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

.By the definition of magnetization, in this model, and in analogy to the physics of springs, the work done per unit volume, in stretching and twisting the bonds between magnetic charge to increment the magnetization by μ0δM is W = H · μ0δM.^No charge will actually flow through the air gap between them, yet a magnetic field will be created in that gap as if the charge were flowing.

.In this model, B = μ0 (H + M ) is an effective magnetization which includes the H-field term to account for the energy of setting up the magnetic field in a vacuum.^Do we have infinite energy in the resulting magnetic field?

This is the correct result, but it is derived from an incorrect model.

.In retrospect the success of this model is due largely to the remarkable coincidence that from the 'outside' the field of an electric dipole has the exact same form as that of a magnetic dipole.^Geometry of the electric and magnetic fields .

.It is therefore only for the physics of magnetism 'inside' of magnetic material where the simpler model of magnetic charges fails.^Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

.It is also important to note that this model is still useful in many situations dealing with magnetic material.^Because so many people use cellular telephones, it is important to learn whether RF radiation affects human health, and to provide reassurance if it does not.

^We have already seen one example of this on page 554, where we inferred that an inductor's time-varying magnetic field creates an electric field --- an electric field which is not created by any charges anywhere.

.The formation of the correct theory of magnetism begins with a series of revolutionary discoveries in 1820, four years before Poisson's model was developed.^Because cancer takes decades to develop, it will be another 10 or 20 years before "mobiles" manifest a bonanza in brain tumors.

.(The first clue that something was amiss, though, was that unlike electrical charges magnetic poles cannot be separated from each other or form magnetic currents.^The electric field of a sheet of charge, and the magnetic field of a sheet of current.

) .The revolution began when Hans Christian Oersted discovered that an electrical current generates a magnetic field that encircles the wire.^The electric field of a sheet of charge, and the magnetic field of a sheet of current.

.In a quick succession that discovery was followed by André-Marie Ampère showing that parallel wires having currents in the same direction attract, and by Jean-Baptiste Biot and Felix Savart developing the correct equation, the Biot–Savart law, for the magnetic field of a current carrying wire.^Any wire that carries an AC electrical current produces magnetic fields.

.In 1825, Ampère extended this revolution by publishing his Ampère's law which provided a more mathematically subtle and correct description of the magnetic field generated by a current than the Biot–Savart law.^Shielding magnetic fields is more difficult than shielding electric fields.

.Subsequent development in the nineteenth century interlinked magnetic and electric phenomena even tighter, until the concept of magnetic charge was not needed.^The electric field of a sheet of charge, and the magnetic field of a sheet of current.

.This development was aided greatly by Michael Faraday, who in 1831 showed that a changing magnetic field generates an encircling electric field.^She observes that a changing magnetic field creates a curly electric field.

.In 1861, James Clerk Maxwell wrote a paper entitled On Physical Lines of Force in which he attempted to explain Faraday's magnetic lines of force in terms of a sea of tiny molecular vortices.^James Clerk Maxwell (1831-1879) .

.These molecular vortices occupied all space and they were aligned in a solenoidal fashion such that their rotation axes traced out the magnetic lines of force.^A diffuse flux of such particles rains down on the Earth all the time, from the depths of space.

^Moreover, if magnetic twists (and currents) extend out far from the star, to regions where outgoing magnetic waves are generated due to the stellar rotation, then they will affect the rate at which the star spins down.

.When two like magnetic poles repel each other, the magnetic lines of force spread outwards from each other in the space between the two poles.^As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

.Maxwell considered that magnetic repulsion was the consequence of a lateral pressure between adjacent lines of force, due to centrifugal force in the equatorial plane of the molecular vortices.^If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

.When deriving the equation for magnetic force in part I of his 1861 paper, Maxwell used a quantity which was closely related to the circumferential speed of the vortices.^To satisfy Maxwell's equations, the time derivatives of the fields must also be twice as large for the blue light.

This quantity was therefore a measure of the vorticity in the magnetic lines of force, and Maxwell referred to it as the intensity of the magnetic force. .In the 1861 paper, the magnetic intensity which we denote as v, was always multiplied by the term μ as a weighting for the cross sectional density of the lines of force.^If the dimensions of the cross-sectional square (height and front-to-back) are b , find the magnetic field (magnitude and direction) along the long central axis.

.The quantity v corresponds reasonably closely to the modern magnetic field vector H, and the product μv corresponds very closely to the modern magnetic flux density B, where μ is referred to as the magnetic permeability.^We can also anticipate that the magnetic field will be a vector.

.Although the classical theory of electrodynamics was essentially complete with Maxwell's equations, the twentieth century saw a number of improvements and extensions to the theory.^Now this is very subtle, because Maxwell's equations treat these charges on an equal basis, but in terms of practical measurements, they are completely different.

^Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

.Albert Einstein, in his great paper of 1905 that established relativity, showed that both the electric and magnetic fields were part of the same phenomena viewed from different reference frames.^In her frame of reference, it's the bar magnet that is moving.

.Both observers see the identical EMF generated in the coil using the flux form of Faraday's law, but explain the result using two different reasons.^Momentum, however, is a vector, and there is only one physically meaningful way of multiplying two vectors to get a vector result, which is the cross product (see page 854).

.All of the charges within the loop move with the loop, and due to the B-field experience a sideways Lorentz force, which generates the EMF. On the other hand, an observer on the loop sees a changing magnetic field due to a moving magnet (relative to the loop's reference frame) and no Lorentz force (charges in the loop are not moving).^Magnetic fields have no sources or sinks.

.Prior to special relativity, it was customary to draw a sharp distinction between these two cases; a stationary magnet and a moving loop only produces motional EMF due to the Lorentz force from the B-field, while a moving magnet through a stationary loop produces only transformer EMF due to the electric field E generated by a changing B.^What is the difference between an electric field and a magnetic field?

See Faraday's law as two different phenomena. Einstein, on the other hand, proposed the equivalence of these two scenarios[32] in the first postulate of relativity that the physics depends on only relative motion. .Motional EMF and transformer EMF, therefore are the same phenomenon as seen in different reference frames.^A charged particle and a current, seen in two different frames of reference.

Important uses and examples of magnetic field

Magnetic circuits

.An important use of H is in magnetic circuits where inside a linear material B = μ H.^If a current of 1.0 A is used, find the magnetic field inside the solenoid if the core is air, and if the core is made of iron with μ/μ o =4,000.

^The result is that when a magnetic field enters a high-permeability material, it tends to twist abruptly to one side, and the pattern of the field tends to be channeled through the material like water through a funnel.

.This result is similar in form to Ohm's lawJ = σ E, where J is the current density, σ is the conductance and E is the electric field.^The Φ E equation is Gauss' law: charges make diverging electric fields.

Extending this analogy we derive the counterpart to the macroscopic Ohm's law ( I = V ⁄ R ) as:

where is the magnetic flux in the circuit, is the magnetomotive force applied to the circuit, and Rm is the reluctance of the circuit. Here the reluctance Rm is a quantity similar in nature to resistance for the flux.

.Using this analogy it is straight-forward to calculate the magnetic flux of complicated magnetic field geometries, by using all the available techniques of circuit theory.^Geometry of the electric and magnetic fields .

Hall effect

.The charge carriers of a current carrying conductor placed in a transverse magnetic field experience a sideways Lorentz force; this results in a charge separation in a direction perpendicular to the current and to the magnetic field.^The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^These lodestones have been charged by the Earth, and thus are harmoniously in tune with the human bodies' frequencies as well, they have for thousands of years been successfully used in the healing arts.

.In the solar dynamo model of the Sun, differential rotation of the solar plasma causes the meridional magnetic field to stretch into an azimuthal magnetic field, a process called the omega-effect.^Dynamos operate in the interior of the Earth and the Sun, giving them their magnetic fields.

.The field strength grows linearly with the radial distance from its longitudinal axis.

A solenoidal magnetic field is similar to a dipole magnetic field, except that a solid bar magnet is replaced by a hollow electromagnetic coil magnet.

A toroidal magnetic field occurs in a doughnut-shaped coil, the electric current spiraling around the tube-like surface, and is found, for example, in a tokamak.

A poloidal magnetic field is generated by a current flowing in a ring, and is found, for example, in a tokamak.

A radial magnetic field is one in which the field lines are directed from the center outwards, similar to the spokes in a bicycle wheel.^If the current is a DC (direct current), the magnetic field is steady, like that form a permanent magnet.

A helical magnetic field is corkscrew-shaped, and sometimes seen in space plasmas such as the Orion Molecular Cloud.^Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.

.From outside, the ideal magnetic dipole is identical to that of an ideal electric dipole of the same strength.^Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

^This is the same as the field of a magnetic dipole in its midplane, except that the electric coupling constant k replaces the magnetic version k / c 2 , and the electric dipole moment D is substituted for the magnetic dipole moment m .

^An electric dipole, unlike a magnetic one, can be built out of two opposite monopoles, i.e., charges, separated by a certain distance, and it is then straightforward to show by vector addition that the field of an electric dipole is .

.An ideal magnetic dipole is modeled as a real magnetic dipole whose area a has been reduced to zero and its current I increased to infinity such that the product m = Ia is finite.^Such a substance, subjected to a magnetic field, tends to align itself, c /2, so that a sheet of current circulates around the externally applied field.

.In this model it is easy to see the connection between angular momentum and magnetic moment which is the basis of the Einstein-de Haas effect "rotation by magnetization" and its inverse, the Barnett effect or "magnetization by rotation".[36] Rotating the loop faster (in the same direction) increases the current and therefore the magnetic moment, for example.^Example 1: The magnetic dipole moment of an atom .

.It is sometimes useful to model the magnetic dipole similar to the electric dipole with two equal but opposite magnetic charges (one south the other north) separated by distance d.^An electric dipole, unlike a magnetic one, can be built out of two opposite monopoles, i.e., charges, separated by a certain distance, and it is then straightforward to show by vector addition that the field of an electric dipole is .

This model produces an H-field not a B-field. .Such a model is deficient, though, both in that there are no magnetic charges and in that it obscures the link between electricity and magnetism.^What is the difference between an electric field and a magnetic field?

.Further, as discussed above it fails to explain the inherent connection between angular momentum and magnetism.^If the braking was due to magnetic waves carrying away energy and angular momentum, as seemed plausible, then the field strength was 8 X 10 14 Gauss.

^Magnetism, as we discussed previously, is an interaction between a moving charge and another moving charge, as opposed to electric forces, which act between any pair of charges, regardless of their motion.

.The north pole of earth is near the top of the diagram, the south pole near the bottom.^Since the distance from the equator to a pole is about 10 7 m, we can estimate, very roughly, that the horizontal component of the earth's magnetic field typically varies by about 10 -11 T/m as you go north or south.

.Notice that the south pole of that magnet is deep in Earth's interior below Earth's North Magnetic Pole.^Since the distance from the equator to a pole is about 10 7 m, we can estimate, very roughly, that the horizontal component of the earth's magnetic field typically varies by about 10 -11 T/m as you go north or south.

.This is the traditional definition of the "north pole" of a magnet, although other equivalent definitions are also possible.^You manage to learn quite a bit of each other's languages, but you're stumped when you try to establish the definitions of left and right (or, equivalently, clockwise and counterclockwise).

.One confusion that arises from this definition is that if Earth itself is considered as a magnet, the south pole of that magnet would be the one nearer the north magnetic pole, and vice-versa.^Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

[37].(Opposite poles attract, so the north pole of the compass magnet is attracted to the south pole of Earth's interior magnet.^Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

) .The north magnetic pole is so named not because of the polarity of the field there but because of its geographical location.^Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.

.The figure to the right is a sketch of Earth's magnetic field represented by field lines.^The current is at right angles to the direction of the changing magnetic field, and is strongest near the extremities of a person.

.For most locations, the magnetic field has a significant up/down component in addition to the North/South component.^Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

.(There is also an East/West component; Earth's magnetic poles do not coincide exactly with Earth's geological pole.^Since the distance from the equator to a pole is about 10 7 m, we can estimate, very roughly, that the horizontal component of the earth's magnetic field typically varies by about 10 -11 T/m as you go north or south.

^A current will not flow through a resistor unless there is some electric field pushing the electrons, so we conclude that the changing magnetic field has produced an electric field in the surrounding space.

^(This field-strength given by a combination of fundamental constants: B Q = m e 2 c 3 / h e , where m e is the mass of the electron, c is the speed of light, h is Planck's constant divided by 2 π, and e is the charge on an electron.

.A permanent magnet in such a field rotates so as to maintain its alignment with the external field.^As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

.This effect was conceptualized by Nikola Tesla, and later utilized in his, and others', early AC (alternating-current) electric motors.^Any wire that carries an AC electrical current produces magnetic fields.

.This inequality would cause serious problems in standardization of the conductor size and so, in order to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference.^Relate λ 2 and v 2 to the current I 2 , using the result of problem 5 a.

.The ability of the three-phase system to create a rotating field, utilized in electric motors, is one of the main reasons why three-phase systems dominate the world's electrical power supply systems.^This electric field is not created by charges .

.Because magnets degrade with time, synchronous motors and induction motors use short-circuited rotors (instead of a magnet) following the rotating magnetic field of a multicoiled stator.^Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

.The short-circuited turns of the rotor develop eddy currents in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.^Magnetic fields are produced by moving electrical currents, and the field of a bar magnet is produced by the spinning electrons around the atomic nuclei in the iron material of the magnet itself.

.In 1882, Nikola Tesla identified the concept of the rotating magnetic field.^A radio pulsar's magnetic field is essentially stable; its main role is to passively facilitate the loss of rotational energy.

In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained U.S. Patent 381,968 for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.

See also

General

Electric field – field produced by electric charges and changing magnetic fields that affects charged particles.

Teltron Tube – device used to display an electron beam and demonstrates effect of electric and magnetic fields on moving charges.

Notes and references

^ Technically, magnetic field is a pseudo vector; pseudo-vectors, which also include torque and rotational velocity, are similar to vectors except that they remain unchanged when the coordinates are inverted.

^ The standard graduate textbook by J. D. Jackson "Classical Electrodynamics" specifically follows the historical tradition, specifically, "In the presence of magnetic materials the dipole tends to align itself in a certain direction. That direction is by definition the direction of the magnetic flux density, denoted by B, provided the dipole is sufficiently small and weak that it does not perturb the existing field". Similarly, in Section 5 of Jackson, H is referred to as the magnetic field. Hence, Edward Purcell, in Electricity and Magnetism, McGraw-Hill, 1963, writes, Even some modern writers who treat B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field", not "magnetic induction." You will seldom hear a geophysicist refer to the Earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H." In a similar vein, M Gerloch (1983). Magnetism and Ligand-field Analysis. Cambridge University Press. p. 110. ISBN 0521249392. http://books.google.com/books?id=Ovo8AAAAIAAJ&pg=PA110. says: “So we may think of both B and H as magnetic fields, but drop the word 'magnetic' from H so as to maintain the distinction … As Purcell points out, 'it is only the names that give trouble, not the symbols'.”

^ The use of iron filings to display a field presents something of an exception to this picture; the filing alter the magnetic field so that it is much larger along the "lines" of iron, due to the large permeability of iron relative to air.

^ To see that this must be true imagine placing a compass inside a magnet. There, the north pole of the compass will point toward the north pole of the magnet since magnets stacked on each other point in the same direction.

^ Two experiments produced candidate events that were initially interpreted as monopoles, but these are now regarded to be inconclusive. For details and references, see magnetic monopole.

^ In special relativity this means that electric and magnetic fields are two parts of the same phenomenon, for a moving charge produces both an electric and a magnetic field. But in a reference frame where the particle is not moving, there is only an electric field. However, the same physics applies to all reference systems. In this reference system, the electric field changes as well to produces the same force as the original reference frame. It is probably a mistake, however, to say that the electric field causes the magnetic field when relativity is taken into account, since relativity favors no particular reference frame. (One could just as easily say that the magnetic field caused an electric field.) More importantly, it is not always possible to move into a coordinate system in which all of the charges are stationary. See classical electromagnetism and special relativity.[citation needed]

^ In practice the Biot–Savart law and other laws of magnetostatics can often be used even when the charge is changing in time as long as it is not changing too quickly. This situation is known as being quasistatic.[citation needed]

^ The Biot–Savart law contains the additional restriction (boundary condition) that the B-field must go to zero fast enough at infinity. It also depends on the divergence of B being zero, which is always valid. (There are no magnetic charges.)

^ A complete expression for Faraday's law of induction in terms of the electric E and magnetic fields can be written as: where ∂Σ(t) is the moving closed path bounding the moving surface Σ(t), and dA is an element of surface area of Σ(t). The first integral calculates the work done moving a charge a distance dℓ based upon the Lorentz force law. In the case where the bounding surface is stationary, the Kelvin–Stokes theorem can be used to show this equation is equivalent to the Maxwell–Faraday equation.

^ College Physics, Volume 10, by Serway, Vuille, and Faughn, page 628 weblink. "the geographic North Pole of Earth corresponds to a magnetic south pole, and the geographic South Pole of Earth corresponds to a magnetic north pole".

Further reading

Web

Nave, R.. ."Magnetic Field Strength H".^Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.

Oppelt, Arnulf (2006-11-02). ."magnetic field strength".^Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.

"magnetic field strength converter".^Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.

The English used in this article or section may not be easy for everybody to understand.You can help Wikipedia by making this page or section simpler.

The Magnetic field is the area around a magnet in which a magnetic force is exerted. Moving electric charges produce magnetic fields. Magnetic fields are usually shown by magnetic flux lines. At all times the direction of the magnetic field is shown by the direction of the magnetic flux lines. The strength of a magnet has to do with the spaces between magnetic flux lines. The closer the flux lines are to each other, the stronger the magnet. The farther apart they are, the weaker the magnet. The flux lines can be seen by placing iron filings over a magnet. Magnetic fields give power to other particles that come in contact with the magnetic field.
In physics, the magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.

When placed in a magnetic field, magnetic dipoles align their axes to be parallel with the field lines, as can be seen when iron filings are in the presence of a magnet. Magnetic fields also have their own energy and momentum, with an energy density proportional to the square of the field intensity. The magnetic field is measured in the units of teslas (SI units) or gauss (cgs units).

There are some notable specific forms of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. For magnetic fields created by changing electric fields, see electromagnetism.

The electric field and the magnetic field are components of the electromagnetic field.